4x(5+y)=10x+8xy

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Solution for 4x(5+y)=10x+8xy equation: 


Simplifying
4x(5 + y) = 10x + 8xy
(5 * 4x + y * 4x) = 10x + 8xy
(20x + 4xy) = 10x + 8xy

Solving
20x + 4xy = 10x + 8xy

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10x' to each side of the equation.
20x + -10x + 4xy = 10x + -10x + 8xy

Combine like terms: 20x + -10x = 10x
10x + 4xy = 10x + -10x + 8xy

Combine like terms: 10x + -10x = 0
10x + 4xy = 0 + 8xy
10x + 4xy = 8xy

Add '-8xy' to each side of the equation.
10x + 4xy + -8xy = 8xy + -8xy

Combine like terms: 4xy + -8xy = -4xy
10x + -4xy = 8xy + -8xy

Combine like terms: 8xy + -8xy = 0
10x + -4xy = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + -2y) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Add '2y' to each side of the equation.
-2y + 2y = -5 + 2y

Combine like terms: -2y + 2y = 0
0 = -5 + 2y

Simplifying
0 = -5 + 2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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